Comparison of two-atom cross spectra in de Sitter spacetime, uniformly accelerated Minkowski vacuum, and a thermal bath
Year: 2026
Type: article
Abstract: We compare two identical two-level atoms coupled to a four-dimensional massless conformally coupled scalar field in three settings: comoving geodesics in the de Sitter Bunch–Davies vacuum, transversely separated uniformly accelerated trajectories in the Minkowski vacuum, and static trajectories in a Minkowski thermal bath. When $$a=H$$ a = H and $$\beta =2\pi /H,$$ β = 2 π / H , their local Wightman kernels and spectra agree in both the excitation and de-excitation sectors. At finite separation, the thermal cross spectrum contains a $$\operatorname {sinc}(\Omega L)$$ sinc ( Ω L ) factor, whereas the two vacuum settings share a hyperbolic geometric factor. At fixed nonzero gap, their large-distance spectral envelopes scale as $$L^{-1}$$ L - 1 and $$L^{-2},$$ L - 2 , respectively. For each fixed midpoint time T , the comoving de Sitter cross kernel equals the accelerated kernel with $$a=H$$ a = H and $$L=r(T).$$ L = r ( T ) . This equality concerns the full relative-time dependence at that midpoint; its Fourier transform is a Wigner-type cross spectrum and is not an instantaneous detector transition rate. We derive the corresponding negative-frequency spectra and express finite-time responses using smooth switching functions. Finite switching samples a range of midpoint times, so matching the two vacuum kernels at one midpoint does not generally match their cross responses over a measurement interval. These relations depend on the specified conformal scalar field and trajectory geometries.
Source: The European Physical Journal C
Author: Zhiming Huang
Institutions: Wuyi University, Wuyi University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7204545501